Challenges and Directions for Knowledge Management in Networks
of Aligned Ontologies
Seremeti Lambrini and Kameas Achilles
School of Science and Technology, Hellenic Open University, Parodos Aristotelous 18, GR-26335, Patras, Greece
Keywords: Ontologies, Alignments, Networks of Aligned Ontologies.
Abstract: Next generation Semantic Web applications have to deal with the real world scenarios of heterogeneous and
distributed knowledge in which collaboration based on knowledge is required. Knowledge is encoded in
semantically rich structures, namely ontologies, while simultaneously, semantic links, that is, alignments are
needed for their successful collaboration. The dynamic unification of a set of ontologies linked by
alignments comprises a network of aligned ontologies. This paper presents some theoretical issues related to
the area of networks of aligned ontologies, aiming at improving practical research directions. More
specifically, we consider here the need, challenges and some guidelines for knowledge representation,
management and propagation within networks of aligned ontologies.
1 INTRODUCTION
Ontologies (Chandrasekaran et al., 1999), (Fonseca,
2007) have been traditionally designed and applied in
applications where knowledge representation is
needed. These ontologies have been constructed as
stand-alone artifacts. For more complex applications,
where knowledge management is required,
ontologies might relate to each other by designing
correspondences between entities of different
ontologies, that is, by constructing alignments
(Euzenat and Shvaiko, 2007). These alignments
constitute the semantic linking among corresponding
ontologies and lead to the development of networked
ontologies.
Towards this end, two trends within the ontology
field have emerged: the ontology networks and the
networks of aligned ontologies. An ontology
network, or a network of ontologies is defined as a
collection of ontologies related together via a variety
of different meta-relationships, such as mapping,
modularization, version and dependency
relationships (Diaz et al., 2011), (Suarez-Figueroa et
al., 2012), whereas a network of aligned ontologies is
defined as a set of ontologies interconnected with
alignments (Euzenat, 2011). Both concepts are used
to organize different types of content by integrating
heterogeneous knowledge sources.
The increasing interest in both ontology networks
and networks of aligned ontologies has a crucial
impact on scientific research, regarding many aspects
of ontology engineering, ontology alignment,
inconsistency detecting, etc. So far, work on
ontology networks mainly refers to how techniques
such as reuse, modularity and modification are
applied on ontologies (Suarez-Figueroa, 2010), while
work on networks of aligned ontologies mainly deals
with consistency checking methods of reasoning
(Fionda and Pirro, 2011).
In this paper, we focus on networks of aligned
ontologies, considering research topics such as
knowledge representation, knowledge management
and knowledge propagation within them. The main
idea behind the appearance of networks of aligned
ontologies is the ability to share and reuse ontologies
and alignments, since designing and maintaining
them is deemed to be a time-consuming and labor
intensive task (Grau et al., 2008), (Beisswanger and
Hahn, 2012).
The remainder of this paper is organized as
follows. Section 2 gives an overview of the
knowledge representation through ontologies within
networks of aligned ontologies, by stating the
challenges that the ontology engineering community
faces. Section 3 underlines the need for
manipulating changes in networks of aligned
ontologies, in order to correctly manage the
knowledge within them. Section 4 describes the
need for propagating knowledge within networks of
aligned ontologies and suggests a formal model for
146
Lambrini S. and Achilles K..
Challenges and Directions for Knowledge Management in Networks of Aligned Ontologies.
DOI: 10.5220/0005044401460152
In Proceedings of the International Conference on Knowledge Management and Information Sharing (KMIS-2014), pages 146-152
ISBN: 978-989-758-050-5
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

achieving this task. Finally, Section 5 deals with
some conclusions and future work.
2 KNOWLEDGE
REPRESENTATION IN
NETWORKS OF ALIGNED
ONTOLOGIES
Knowledge representation in networks of aligned
ontologies involves ontologies that represent
different pieces of knowledge and alignments that
represent the semantic correlation of the
corresponding ontologies.
2.1 Need
Applications in open, dynamic and distributed
environments, such as the Semantic Web need to
share resources. These applications involve
autonomous entities which have been designed
independently (Euzenat et al., 2008), (Pruvost et al.,
2009) thus facing a high level of heterogeneity. On
the one hand, this is desirable, as it allows the
involved parties to structure knowledge in a way
fitting their needs best, e.g., regarding a specific
application. On the other hand, this becomes
problematic, as it impedes the involved parties’
communication because knowledge of the resources
is encoded in a variety of ways. One aspect of
overcoming heterogeneity in order for the involved
entities to interoperate in these environments, is an
explicit and semantically rich representation of
knowledge through ontologies. Ontologies aim at
capturing domain knowledge in an explicit way and
they provide a consensual understanding of the
domain (de Bruijn, 2003). Because it is impractical
for all the involved entities to share a unique and
global ontology, a plethora of individual ontologies
have recently emerged, some of them representing
overlapping content (Euzenat et al., 2008). Thus, the
fact of using different ontologies increases
heterogeneity problems to a different level.
Semantic alignment between ontologies is a
solution to the heterogeneity problem. It can be
considered as the result of the ontology matching
process, which deals with finding the
correspondences between semantically related
entities of different ontologies (Ehrig, 2007). The
existence of a semantic alignment between
ontologies is a necessary precondition to establish
interoperability between the involved entities using
different individual ontologies. Moreover, human
users want to access the knowledge represented in
numerous different ontologies in order to ease the
tasks of searching, or browsing. In addition, new
knowledge can be inferred by combining the
information contained in the various ontologies.
Thus, ontology alignment is a crucial issue to
resolve in any application involving more than one
entities, or parties, where semantic heterogeneity is
an intrinsic problem (Shvaiko and Euzenat, 2013).
Once semantic alignments have been established
between individual ontologies, a network of linked
ontologies can be created. In this setting, ontologies
represent different knowledge sources participating
in the network, and alignments represent the
semantic links between these sources.
2.2 Challenge
Constructing networks of aligned ontologies
typically consists of dynamically assembling their
components, that is, ontologies and alignments, in
such a way that the overall structure entails new
knowledge. Since such components are authored in
different context, unaware of what other a posteriori
formal knowledge they will be combined with, the
challenge is to provide guidance for separately
engineering ontologies and alignments, instead of
proposing a unified model for the construction of
networks of aligned ontologies. There are also many
challenges regarding ontology engineering,
especially ontology reuse. Moreover, there is little
support, in the ontology matching process, regarding
the selection of suitable matchers in order to produce
correct alignments.
2.3 Suggestion
In this perspective, on the one hand, an ontology
engineering approach is needed, which must
emphasize on the availability of knowledge sources
to be used (Terrazas, 2011). On the other hand, an
ontology alignment strategy with emphasis on the
selection of the suitable matchers and the
involvement of a trusted third party in order to
ensure the generation of reliable alignments
(Kameas and Seremeti, 2011), is needed.
3 KNOWLEDGE MANAGEMENT
IN NETWORKS OF ALIGNED
ONTOLOGIES
Knowledge management in networks of aligned
ontologies consists of managing changes that
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occurred in their constituents (ontologies and
alignments).
3.1 Need
Networks of aligned ontologies are defined as
directed graphs, consisting of vertices representing
heterogeneous ontologies and edges representing
alignments among them. Both their autonomous
components, which have been designed
independently, are carriers of meaning. On the one
hand, ontologies convey semantics, since they are
defined as the formal conceptualizations of a domain
of interest (Studer et al., 1998). On the other hand,
alignments are defined as the links that semantically
relate two formal conceptualizations (Scharffe et al.,
2008). As both components describe parts of the
world and their interconnections, they may undergo
changes, due to the dynamic nature of the describing
world. These changes, despite the fact that they may
occur in isolated components, they may result in an
inconsistent state for the overall network of
interlinked components.
3.2 Challenge
The facts that new ontologies can be embedded in a
network of already aligned ones, or can be removed
from such a network and that ontologies and/or
alignments between them have to be kept up to date
in changing application contexts, are some of the
factors that are involved in the definition of the
dynamic engineering of networks of aligned
ontologies. Moreover, in order to take into account
the fact that making changes based on isolated
entities, while ignoring the semantic interrelations
among them, may result in an inconsistent state for
the underlying semantic model, we consider a
twofold view of such networks: a local and a global
one. The local view refers to isolated entities, that is,
ontologies and alignments, while the global one
refers to the context in which the separate
components are interconnected in a way that
explicitly characterizes the semantics of a specific
application. Thus, to define change operations in
networks of aligned ontologies, one has to take into
account, not only all the possible effects a change
can have on its separate components, but also its
influence on the hypostasis of the networks
themselves.
3.3 Suggestion
With respect to the aforementioned views of a
network of aligned ontologies, we claim that
significant improvements in managing it can be
obtained, by addressing important challenges for
manipulating changes in three interrelated levels:
 The ontology level, which represents changes
in the ontologies, namely the changes in their
domain of usage, (since most domains have a
dynamic nature), changes in their level of
formality and/or their level of granularity.
More precisely, Klein (Klein, 2004)
distinguishes among three kinds of changes
that may occur within an ontology, i.e.,
conceptual, specification and representation
changes;
 The alignment level, which represents changes
in the definition of alignments between the
same pair of ontologies, for example by
applying a different matching algorithm, or by
using an alternative representation language
(Ehrig, 2007);
 The network level, which represents changes in
the number and the content of the ontologies
that participate in a network of aligned
ontologies. For example, a new ontology must
be added to a network of previous aligned
ontologies, or must be removed from the
network, according to the requirements
imposed by a specific application (Kameas
and Seremeti, 2011).
From an engineering point of view, changes at
the ontology level refer to the ontology evolution
and versioning processes (Yildiz, 2006), (Jaziri,
2009), which are based on discovering semantic
relations among entities of two versions of the same
ontology and require the ontology alignment
process. Changes at the alignment level refer to the
alignment versioning process (Euzenat and Shvaiko,
2007), which aims at finding out relations among
two versions of the same alignment, while, changes
at the network level require the definition of an
ontology alignment composition operator
(Zimmermann and Le Duc, 2008).
4 KNOWLEDGE PROPAGATION
IN NETWORKS OF ALIGNED
ONTOLOGIES
A network of aligned ontologies is a distributed
system, whose components (constituent ontologies)
are interacting and interoperating, the result of this
interaction being, either the extension of local
assertions, which are valid within each individual
ontology, to global assertions holding between
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remote ontology entities through a network path, or
to local assertions holding between local entities of
an ontology, but induced by remote ontologies,
through a cycle. In order to describe this interaction,
we use knowledge propagation.
4.1 Need
Consider for example the network of Figure 1, where
the relationships between entities
i
a
,
i
b
,
i
c
,
i
d
of
ontologies
1
O
,
2
O
and
3
O
are considered to be, either
subsumption (
 ) or disjointness (  ) ones. We also
consider the alignments
12
A
(between entities of
1
O
and
2
O
),
23
A
(between
2
O
and
3
O
) and
31
A
(between
3
O
and
1
O
), where the relations involved
between entities belonging to different ontologies are
subsumption relationships. Induced relations,
resulting from composition of relations, are marked
with dotted lines. In this network, new relations can
be deduced, for example by either relating
ontological entities belonging to remote ontologies
1
O
and
3
O
through the particular path
112 2 23 3
OA O A O
of ontologies and alignments
in the network, or by relating ontological entities
belonging to the same ontology, but through a
particular path forming a loop starting and ending at
this specific ontology. This is for example the case
for the loop
331112 2233
OAOAOA O
, where
the relations revealed make apparent consistency
problems emerging from the network induced
relations, as will be evident in Section 4.3.
1
a
1
b
1
c

1
O

2
a
2
b
2
c

2
O



12
A
3
a
3
b
3
c

3
O


3
d
23
A


31
A


Figure 1: An example of a network of aligned ontologies.
4.2 Challenge
Thus, a crucial issue is: while propagating local
knowledge through the network, one should be able
to retain the consistency of the whole network and
extract meaningful results from the global
knowledge emerging from a particular network of
aligned ontologies.
4.3 Suggestion
Significant improvements can be obtained only by
addressing the important issue of formalizing the
basic building blocks of networks of aligned
ontologies (constituent ontologies and alignments)
and the propagation of knowledge within them, in a
way independent from their language representation
and implementation. In order to be able to propagate
relations in a network of ontologies and alignments,
we define a matrix representation of an ontology, or
an alignment, where we represent the ontology, or
alignment by a so-called propagation matrix.
This representation depends strongly on the
specific position that an ontology occupies in a chain
of ontologies and alignments that forms a path of
consecutive ontologies and alignments in the network
More specifically, we differentiate the representation
according to whether an ontology is a starting node
involved only in a succeeding alignment, or a
transition node involved in both a preceding and a
succeeding alignments, or, finally, an ending node
involved only in a preceding alignment. Alignments
can also be represented in an analogous manner as
the one adopted for ontologies, since an alignment
between two ontologies relates entities of the
preceding source ontology to entities of the
succeeding target ontology.
In these propagation matrix representations, we
express local relations between ontology entities that
can be further propagated through the path. More
precisely, for ontologies that are starting nodes in the
path, these are local relations further propagated in
the network through the succeeding alignment; for
ontologies that are transition nodes these are local
relations that can be composed with relations arriving
to the ontology via the preceding alignment and can
be further propagated in the network via the
succeeding alignment; for ontologies that act as
ending nodes, these are local relations that can be
composed with relations arriving to the ontology via
the preceding alignment. In general, the element


,kl of the propagation matrix representation
corresponds to the composition of relations holding
along all the paths connecting the source ontology
entity
k to the target ontology entity l . In the
th
l
column of the propagation matrix we find all the
compositions of relations along all the paths having
as source object some entity of the ontology and
having
l as the target entity. This corresponds to all
the incoming arrows to object
l , and can be
represented by the notion of contravariant
representable functors, a construct in the formalism
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149

based on Category Theory (Barr and Wells, 2012). A
category is a structure consisting of a collection of
objects and a collection of morphisms between
objects, equipped with an associative composition
operator and a unique morphism associated to each
object, acting as the unit of the composition. Given a
category and a fixed object, say
A , in that category,
the contravariant representable functor maps a certain
object, say
C , in the category, to the set of all
morphisms from
C to A , i.e. it refers to all
incoming morphisms to the fixed object
A
and
categorizes them according to the object which is the
origin of the morphism.
Category Theory has been extensively used as an
appropriate framework for the formalization of
ontologies and their operations (Zimmermann et al.,
2006), (Euzenat, 2011), (Diskin and Maibaum,
2012), (Spivak and Kent, 2012), where “local truth”
vs. “global truth” in a network is studied by defining
and combining several categorical structures.The
propagation matrices can be combined along
sequential or parallel paths, by defining adequate
operators. For this purpose we define a sequential
composition operator denoted as
 and a parallel
composition operator denoted as  . The sequential
composition operator resembles the usual matrix
multiplication operator, where multiplication has
been substituted by relation composition and addition
by the disjunction of relations. The sequential
composition operator can be applied repeatedly along
a chain of ontologies and alignments that define a
path in a network of ontologies, in order to propagate
local knowledge to global one. When two ontologies
in the network are connected through a number of
different paths, the parallel composition operator is
used. This increases expressiveness, since now
entities can be related through any possible relation
belonging to a set of available ones composable over
a suitable algebra of binary relations, and which
could be more elaborate than the usual subsumption
relations.
In the example of Figure 1, we calculate the
propagation matrix through the path (cycle)
331112 2233
OAOAOAO
by repeatedly applying
the sequential operator over the individual
propagation matrices, respectively:
 
00
00 0 1
1000
10 0 0
01

  










Since for example
3
O
is a starting node in this path,
its respective propagation matrix
33
3
3
3
3
00
00
10
01
cd
a
b
c
d












expresses the relations between from one part the
entities
3
a
,
3
b
,
3
c
,
3
d
and from the other part the
entities
3
c
,
3
d
, these being the only relations that can
be further propagated in the network. Concerning the
alignment
31
A
, the respective propagation matrix
11
3
3
0
0
bc
c
d








expresses the relations holding between
3
c
,
3
d
of
3
O
and
1
b
,
1
c
of
1
O
. Here, 0 denotes the absence of
relation between the respective elements and
1 the
unity element of the composition of relations. By
adequately composing the binary relations over an
adequate algebra of binary relations, one gets:
333 3
3
3
3
3
0000
0000
0000
000
abcd
a
b
c
d













from where the relation
33
da

results. From the local
knowledge of ontology
3
O
, we obtain:
333 3
3
3
3
3
1000
100
010
01
abcd
a
b
c
d















from where the relation
33
da

results. When the two
propagation matrices are considered conjuctively, the
inconsistency between the relations
33
da
and
33
da

is revealed.
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5 CONCLUSIONS AND FUTURE
WORK
Ontologies are no longer stand-alone artifacts, but
they are linked through alignments in order to
support semantically enabled applications. Towards
this end, a new trend within the ontology field has
emerged: the network of aligned ontologies. The
appearance of networks of aligned ontologies is due
to the achievements of the ontology community
about ontologies and alignments reuse and evolution.
In this paper, we focused on (a) ontologies and
alignments as the constituent components of
networks of aligned ontologies, in order to obtain
knowledge representation within such settings, (b)
changes occurred in the ontology, alignment and
network level, in order to manage evolving
knowledge, and (c) suggesting a mathematical
formalization for achieving knowledge propagation,
in order to detect inconsistency within them. We
presented some challenges with insights on how to
approach them, thereby aiming to facilitate the
progress in the field.
As far as future research is concerned, we envisage
the direction of implementing algorithms based on
Category Theory, and especially on contravariant
representable functors, for representing, managing
and propagating knowledge within networks of
aligned ontologies. This will contribute in detecting
conceptual errors in order to revise the knowledge
emerging from the whole network.
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